Geometry

Question Analysis  

The main focus is to determine the equation of the directrix of a parabola using the given focus and vertex, identifying its orientation and key parameters.  

 

Key Concept Explanation  

Vertical Parabola Directrix: For a parabola with vertex at the origin and focus , the parabola is vertical. The directrix is a horizontal line , equidistant from the vertex as the focus but in the opposite direction.  

 

Step-by-Step Solution  

1. Identify orientation and :  

Vertex: , Focus: .  

Both lie on the -axis, so the parabola is vertical.  

The focus is at , so (negative, indicating the parabola opens downward).  

2. Determine the directrix:  

For a vertical parabola, the directrix is